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// Copyright John Maddock 2006.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_STATS_WEIBULL_HPP
#define BOOST_STATS_WEIBULL_HPP
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
// http://mathworld.wolfram.com/WeibullDistribution.html
#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/math/distributions/complement.hpp>
#include <utility>
namespace boost{ namespace math
{
namespace detail{
template <class RealType, class Policy>
inline bool check_weibull_shape(
const char* function,
RealType shape,
RealType* result, const Policy& pol)
{
if((shape <= 0) || !(boost::math::isfinite)(shape))
{
*result = policies::raise_domain_error<RealType>(
function,
"Shape parameter is %1%, but must be > 0 !", shape, pol);
return false;
}
return true;
}
template <class RealType, class Policy>
inline bool check_weibull_x(
const char* function,
RealType const& x,
RealType* result, const Policy& pol)
{
if((x < 0) || !(boost::math::isfinite)(x))
{
*result = policies::raise_domain_error<RealType>(
function,
"Random variate is %1% but must be >= 0 !", x, pol);
return false;
}
return true;
}
template <class RealType, class Policy>
inline bool check_weibull(
const char* function,
RealType scale,
RealType shape,
RealType* result, const Policy& pol)
{
return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
}
} // namespace detail
template <class RealType = double, class Policy = policies::policy<> >
class weibull_distribution
{
public:
typedef RealType value_type;
typedef Policy policy_type;
weibull_distribution(RealType l_shape, RealType l_scale = 1)
: m_shape(l_shape), m_scale(l_scale)
{
RealType result;
detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
}
RealType shape()const
{
return m_shape;
}
RealType scale()const
{
return m_scale;
}
private:
//
// Data members:
//
RealType m_shape; // distribution shape
RealType m_scale; // distribution scale
};
typedef weibull_distribution<double> weibull;
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
{ // Range of permissible values for random variable x.
using boost::math::tools::max_value;
return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
}
template <class RealType, class Policy>
inline const std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
{ // Range of supported values for random variable x.
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
using boost::math::tools::max_value;
using boost::math::tools::min_value;
return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
// A discontinuity at x == 0, so only support down to min_value.
}
template <class RealType, class Policy>
inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
if(false == detail::check_weibull_x(function, x, &result, Policy()))
return result;
if(x == 0)
{
if(shape == 1)
{
return 1 / scale;
}
if(shape > 1)
{
return 0;
}
return policies::raise_overflow_error<RealType>(function, 0, Policy());
}
result = exp(-pow(x / scale, shape));
result *= pow(x / scale, shape - 1) * shape / scale;
return result;
}
template <class RealType, class Policy>
inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
if(false == detail::check_weibull_x(function, x, &result, Policy()))
return result;
result = -boost::math::expm1(-pow(x / scale, shape), Policy());
return result;
}
template <class RealType, class Policy>
inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
if(false == detail::check_probability(function, p, &result, Policy()))
return result;
if(p == 1)
return policies::raise_overflow_error<RealType>(function, 0, Policy());
result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
return result;
}
template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
RealType shape = c.dist.shape();
RealType scale = c.dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
return result;
result = exp(-pow(c.param / scale, shape));
return result;
}
template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
RealType shape = c.dist.shape();
RealType scale = c.dist.scale();
RealType q = c.param;
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
if(false == detail::check_probability(function, q, &result, Policy()))
return result;
if(q == 0)
return policies::raise_overflow_error<RealType>(function, 0, Policy());
result = scale * pow(-log(q), 1 / shape);
return result;
}
template <class RealType, class Policy>
inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
return result;
}
template <class RealType, class Policy>
inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
{
RealType shape = dist.shape();
RealType scale = dist.scale();
static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
{
return result;
}
result = boost::math::tgamma(1 + 1 / shape, Policy());
result *= -result;
result += boost::math::tgamma(1 + 2 / shape, Policy());
result *= scale * scale;
return result;
}
template <class RealType, class Policy>
inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
{
BOOST_MATH_STD_USING // for ADL of std function pow.
static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
{
return result;
}
if(shape <= 1)
return 0;
result = scale * pow((shape - 1) / shape, 1 / shape);
return result;
}
template <class RealType, class Policy>
inline RealType median(const weibull_distribution<RealType, Policy>& dist)
{
BOOST_MATH_STD_USING // for ADL of std function pow.
static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
RealType shape = dist.shape(); // Wikipedia k
RealType scale = dist.scale(); // Wikipedia lambda
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
{
return result;
}
using boost::math::constants::ln_two;
result = scale * pow(ln_two<RealType>(), 1 / shape);
return result;
}
template <class RealType, class Policy>
inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
{
return result;
}
RealType g1, g2, g3, d;
g1 = boost::math::tgamma(1 + 1 / shape, Policy());
g2 = boost::math::tgamma(1 + 2 / shape, Policy());
g3 = boost::math::tgamma(1 + 3 / shape, Policy());
d = pow(g2 - g1 * g1, RealType(1.5));
result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
return result;
}
template <class RealType, class Policy>
inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
{
BOOST_MATH_STD_USING // for ADL of std functions
static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
RealType shape = dist.shape();
RealType scale = dist.scale();
RealType result = 0;
if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
return result;
RealType g1, g2, g3, g4, d, g1_2, g1_4;
g1 = boost::math::tgamma(1 + 1 / shape, Policy());
g2 = boost::math::tgamma(1 + 2 / shape, Policy());
g3 = boost::math::tgamma(1 + 3 / shape, Policy());
g4 = boost::math::tgamma(1 + 4 / shape, Policy());
g1_2 = g1 * g1;
g1_4 = g1_2 * g1_2;
d = g2 - g1_2;
d *= d;
result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
result /= d;
return result;
}
template <class RealType, class Policy>
inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
{
return kurtosis_excess(dist) + 3;
}
} // namespace math
} // namespace boost
// This include must be at the end, *after* the accessors
// for this distribution have been defined, in order to
// keep compilers that support two-phase lookup happy.
#include <boost/math/distributions/detail/derived_accessors.hpp>
#endif // BOOST_STATS_WEIBULL_HPP